Scale-Spaces provide a way of organizing and analyzing all scales of an object in a single structure.

The linear scale-space of an image is the solution of the diffusion equation (with the image as the initial condition). This scale-space is built through applying the gaussian filter with increasing variances to the image. As a result, a three-dimensional structure of blurry images is obtained.

In this thesis, the main theoretical properties of continuous and discrete linear scale-spaces are
described, as well as several types of discrete scale-spaces, such as sampled gaussian, Poisson,
recursive gaussian, crossed convolution, splines and infinitesimal generator. Also, specific details of the discrete scale-spaces implementation are examined.

The thesis continues analyzing the methods of edge detection - including its implementation - starting from an image and starting from the multi-scale analysis of an image.